Related papers: Compositional Hoare-style Reasoning about Hybrid C…
The general completeness problem of Hoare logic relative to the standard model $N$ of Peano arithmetic has been studied by Cook, and it allows for the use of arbitrary arithmetical formulas as assertions. In practice, the assertions would…
Temporal logic provided an appealing approach to specifying properties of operating systems and other "reactive" software by allowing propositions to be qualified by "when" they must be true. This paper shows how to get the same effect,…
Abstract separation logics are a family of extensions of Hoare logic for reasoning about programs that manipulate resources such as memory locations. These logics are "abstract" because they are independent of any particular concrete…
While software requirements are often expressed in natural language, verifying the correctness of a program against such requirements is a hard and underexplored problem. Large language models (LLMs) are promising candidates for addressing…
We develop a formal framework for the behavioral comparison of linear systems across different time domains. We accomplish this by introducing the notion of system interpolation, which determines whether the input-state trajectories of a…
Cminor is a mid-level imperative programming language; there are proved-correct optimizing compilers from C to Cminor and from Cminor to machine language. We have redesigned Cminor so that it is suitable for Hoare Logic reasoning and we…
Clocked Cubical Type Theory is a new type theory combining the power of guarded recursion with univalence and higher inductive types (HITs). This type theory can be used as a metalanguage for synthetic guarded domain theory in which one can…
Linear-time computational techniques have been developed for combining evidence which is available on a number of contending hypotheses. They offer a means of making the computation-intensive calculations involved more efficient in certain…
The need for rigorous process composition is encountered in many situations pertaining to the development and analysis of complex systems. We discuss the use of Classical Linear Logic (CLL) for correct-by-construction resource-based process…
In this paper, we investigate the model checking (MC) problem for Halpern and Shoham's interval temporal logic HS. In the last years, interval temporal logic MC has received an increasing attention as a viable alternative to the traditional…
Previous results on proving confluence for Constraint Handling Rules are extended in two ways in order to allow a larger and more realistic class of CHR programs to be considered confluent. Firstly, we introduce the relaxed notion of…
In this paper, we present a mechanism for building hybrid system observers to differentiate between specific positions of the hybrid system. The mechanism is designed through inferring metric temporal logic (MTL) formulae from simulated…
Process calculi based on logic, such as $\pi$DILL and CP, provide a foundation for deadlock-free concurrent programming. However, in previous work, there is a mismatch between the rules for constructing proofs and the term constructors of…
Verification is crucial for effective mathematical reasoning. We present a new temporal consistency method where verifiers iteratively refine their judgments based on the previous assessment. Unlike one-round verification or multi-model…
In this paper a novel hybrid approach for compensating the distortion of any interpolation has been proposed. In this hybrid method, a modular approach was incorporated in an iterative fashion. By using this approach we can get drastic…
This paper provides a compositional scheme based on dissipativity approaches for constructing finite abstractions of continuous-time continuous-space stochastic control systems. The proposed framework enjoys the structure of the…
Hybrid systems are a compact and natural mechanism with which to address problems in robotics. This work introduces an approach to learning hybrid systems from demonstrations, with an emphasis on extracting models that are explicitly…
Hybrid logic extends modal logic with support for reasoning about individual states, designated by so-called nominals. We study hybrid logic in the broad context of coalgebraic semantics, where Kripke frames are replaced with coalgebras for…
Linear type theories, of various types and kinds, are of fundamental importance in most programming language research nowadays. In this paper we describe an extension of Benton's Linear-Non-Linear type theory and model for which we can…
We present a calculus providing a Curry-Howard correspondence to classical logic represented in the sequent calculus with explicit structural rules, namely weakening and contraction. These structural rules introduce explicit erasure and…